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loris [4]
4 years ago
13

Let v = (v1, v2) be a vector in r2. show that (v2, −v1) is orthogonal to v, and use this fact to find two unit vectors orthogona

l to the given vector. v = (9, 40)
Mathematics
2 answers:
hodyreva [135]4 years ago
3 0
Because v1 x v2 + v2 x (-v1) = v1 x v2 - v2 x v1 = v1 x v2 - v1 x v2 = 0, vector (v1,v2) is orthogonal to (v2,-v1);
Let (a,b) be an unit vector orthogonal to (9,40);
So, a^2 + b^2 = 1 and a x 9 + b x 40 = 0;
Then, a = - 40 x b / 9;
Finally, 160 x b^2 / 81 + b^2 = 1;
160 x b^2 + 81 x b^2 = 81;
241 x b^2 = 81;
b^2 = 81 / 241;
b = + or - 9/\sqrt{241}
a = + or - 40/\sqrt{241}
We have (+40/\sqrt{241};9/\sqrt{241}) and (-40/\sqrt{241};-9/\sqrt{241});
Maslowich4 years ago
3 0

Answer:

\hat{u_1}=(\frac{40}{41},-\frac{9}{40}) and \hat{u_2}=(\frac{-40}{41},\frac{9}{41})

Step-by-step explanation:

We are given that v=(v_1,v_2) be a vector in R^2.

We have to show that (v_2,-v_1) is orthogonal to v.We have to find the two unit vector orthogonal to the given vector v=(9,40).

Orthogonal vectors:If two vectors u and v are orthogonal then

u\cdot v=u_1v_2+u_2v_1=0

Using this condition

(v_1,v_2)\cdot (v_2,-v_1)

=v_1v_2-v_2v_1=0

Hence, (v_2,-v_1) is orthogonal to v.

By using this fact then, we get

u_1=(40,-9) is orthogonal to v=(9,40)

Unit vector=\frac{\vec{a}}{\mid a\mid}

\mid u_1\mid=\sqrt{(40)^2+(-9)^2}=41

\hat{u_1}=(\frac{40}{41},-\frac{9}{40})

u_2=(-40,9) is orthogonal to v=(9,40)

\mid u_2\mid=\sqrt{(-40)^2+9^2}=41

\hat{u_2}=(\frac{-40}{41},\frac{9}{41})

The two unit vectors which are orthogonal to given vector v=(9,40) are given by

\hat{u_1}=(\frac{40}{41},-\frac{9}{40}) and \hat{u_2}=(\frac{-40}{41},\frac{9}{41})

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5 0
3 years ago
Confusing stuff! Giving out 50 big points!
UkoKoshka [18]
If the gum costs 75 cents today, which is 3 cents less than three times what the pack cost 20 years ago, we just need to arrange what we know into an equation.
We know that the price of gum today is 75 cents, so we can leave that on one side of the equation as a constant. Also, since we are dealing only with cents and not dollars, there is no need to shift the decimal point to the left.

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Now, we can work the equation.

The problem tells us that 75 is 3 cents less than three times the old cost. So, if x is the old cost, we can work out the equation based on that.
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7 0
3 years ago
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If f(x) = x-6 and g(x)=x1/2(x+3)and g(x)Xf(x)<br> please help me
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Answer:

I believe the answer is A

Step-by-step explanation:

Hope this helps!

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